02_Exploratory_Data_Analysis

1 Exploratory Data Analysis (EDA)

This document presents an exploratory data analysis of critical elements concentration data, which provide information about the concentration of critical mineral across different areas in Australia that has been normalised using PAAS (Post-Archean Australian Shale) standard. The primary objective of this analysis is to gain a deeper understanding of the data’s structure and key characteristics. Through this, we aim to identify significant trends, correlations, and outliers that may influence the outcomes of the study.

1.1 Data General Characteristics

Our data comprises of 11032 observations and 8 variables. Most of the variables are character type, except for variable Element_Value_ppm, PAAS_value_ppm, and PAAS_normalised_value that are numeric type.

## Classes 'data.table' and 'data.frame':   11032 obs. of  8 variables:
##  $ Project_Name         : chr  "Collingwood Park" "Confidential_B" "Confidential_B" "Confidential_B" ...
##  $ Sample_ID            : chr  "CP-014" "ICP23000472Z291" "ICP23000472Z292" "ICP23000472Z293" ...
##  $ Element_Symbol       : chr  "Ag" "Ag" "Ag" "Ag" ...
##  $ Element_Value_ppm    : num  0.13 0.14 0.11 0.11 0.11 0.11 0.11 0.11 0.15 0.5 ...
##  $ Element_Description  : chr  "Silver" "Silver" "Silver" "Silver" ...
##  $ PAAS_value_ppm       : num  0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 ...
##  $ PAAS_normalised_value: num  2.6 2.8 2.2 2.2 2.2 2.2 2.2 2.2 3 10 ...
##  $ Above_PASS_flag      : chr  "Enriched above background" "Enriched above background" "Enriched above background" "Enriched above background" ...
##  - attr(*, ".internal.selfref")=<externalptr>

The Table 1.1 provide a preview of the data from the first ten observations.

Table 1.1: The first ten observations of the data

Project Name	Sample ID	Element Symbol	Element Value ppm	Element Description	PAAS value ppm	PAAS normalised value	Above PASS flag
Collingwood Park	CP-014	Ag	0.13	Silver	0.05	2.6	Enriched above background
Confidential_B	ICP23000472Z291	Ag	0.14	Silver	0.05	2.8	Enriched above background
Confidential_B	ICP23000472Z292	Ag	0.11	Silver	0.05	2.2	Enriched above background
Confidential_B	ICP23000472Z293	Ag	0.11	Silver	0.05	2.2	Enriched above background
Confidential_B	ICP23000472Z294	Ag	0.11	Silver	0.05	2.2	Enriched above background
Confidential_B	ICP23000472Z299	Ag	0.11	Silver	0.05	2.2	Enriched above background
Confidential_B	ICP23000472Z300	Ag	0.11	Silver	0.05	2.2	Enriched above background
Confidential_B	ICP23000472Z301	Ag	0.11	Silver	0.05	2.2	Enriched above background
Confidential_B	ICP23000472Z302	Ag	0.15	Silver	0.05	3.0	Enriched above background
Confidential_C	IP23005174R1046	Ag	0.50	Silver	0.05	10.0	Enriched above background

1.2 Descriptive Statistics

In this section, we will provide some generic statistics information about the data, such as min, max, mean, median, and others. The Table 1.2 lay out the details about these informations for each critical element that is included in the data.

Table 1.2: Descriptive Statistics of Elements’ Normalised Value

Element Symbol	Element Description	min	max	mean	median	range	q1	q3	iqr	sd	var	skewness	kurtosis
Ag	Silver	0.100	0.660	0.207	0.180	0.560	0.110	0.272	0.163	0.119	0.014	1.647	5.783
Al	Aluminium	7.210	680,000.000	67,579.252	35,000.000	679,992.790	17,000.000	103,000.000	86,000.000	78,592.423	6,176,769,029.641	4.403	34.192
Au	Gold	0.001	0.022	0.006	0.006	0.021	0.004	0.008	0.004	0.004	0.000	1.806	7.764
Ba	Barium	7.000	10,000.000	609.458	412.500	9,993.000	189.750	653.250	463.500	1,114.878	1,242,952.531	5.997	43.446
Be	Beryllium	0.100	18.000	3.377	2.000	17.900	1.000	4.000	3.000	3.401	11.564	1.981	7.156
Bi	Bismuth	0.100	3.200	0.468	0.305	3.100	0.200	0.600	0.400	0.419	0.176	3.012	17.818
Cd	Cadmium	0.010	0.720	0.125	0.090	0.710	0.050	0.185	0.135	0.109	0.012	2.075	9.839
Ce	Cerium	3.600	380.000	61.211	63.050	376.400	31.125	81.375	50.250	38.062	1,448.728	2.362	21.060
Co	Cobalt	2.000	134.000	15.400	10.000	132.000	6.000	15.250	9.250	19.268	371.261	3.617	17.661
Cr	Chromium	1.000	897.000	36.565	17.000	896.000	11.000	29.000	18.000	86.951	7,560.393	6.622	54.642
Cs	Caesium	0.110	31.600	4.915	4.245	31.490	2.445	6.357	3.912	4.188	17.540	2.460	12.858
Cu	Copper	1.000	255.000	42.025	47.000	254.000	16.000	60.750	44.750	28.991	840.485	1.617	13.140
Dy	Dysprosium	0.400	18.500	5.325	5.310	18.100	3.500	6.715	3.215	2.965	8.790	1.115	5.566
Er	Erbium	0.200	11.400	3.222	3.035	11.200	2.000	4.072	2.072	1.875	3.517	1.300	6.383
Eu	Europium	0.100	6.840	1.474	1.450	6.740	0.800	1.920	1.120	0.852	0.727	1.295	8.535
Fe	Iron	0.190	339,126.000	16,595.088	6,301.000	339,125.810	2,000.000	15,000.000	13,000.000	37,320.398	1,392,812,116.408	5.788	45.053
Ga	Gallium	1.300	52.300	21.981	21.950	51.000	12.900	31.625	18.725	11.620	135.019	-0.020	2.148
Gd	Gadolinium	0.500	25.100	6.038	5.750	24.600	3.600	7.555	3.955	3.424	11.725	1.380	7.420
Ge	Germanium	0.140	70.000	11.970	0.550	69.860	0.292	15.200	14.907	20.849	434.698	1.458	3.653
HREE	Ho+Er+Tm+Yb+Lu	1.100	30.600	8.671	8.200	29.500	5.462	10.753	5.290	4.812	23.153	1.374	6.712
Ho	Holmium	0.100	3.800	1.081	1.045	3.700	0.700	1.355	0.655	0.613	0.376	1.187	5.962
In	Indium	0.020	0.360	0.072	0.050	0.340	0.030	0.100	0.070	0.056	0.003	2.167	9.581
LREE	La+Ce+Pr+Nd+Pm+Sm	11.700	554.500	134.275	140.060	542.800	81.100	180.300	99.200	71.054	5,048.606	0.837	6.992
La	Lanthanum	3.000	76.200	26.129	27.900	73.200	12.000	36.000	24.000	14.409	207.612	0.155	2.566
Li	Lithium	5.000	285.000	47.724	40.000	280.000	15.000	64.500	49.500	39.486	1,559.133	1.860	9.533
Lu	Lutetium	0.000	2.000	0.493	0.460	2.000	0.300	0.610	0.310	0.294	0.087	1.420	7.067
MREE	Eu+Gd+Tb+Dy+Y	2.700	135.100	41.948	41.410	132.400	24.700	52.330	27.630	23.288	542.320	1.200	5.952
Mn	Manganese	1.000	11,230.000	356.239	65.500	11,229.000	19.000	220.500	201.500	1,130.209	1,277,371.401	7.302	66.528
Mo	Molybdenum	0.100	20.600	4.456	4.000	20.500	2.000	5.000	3.000	3.292	10.836	2.227	10.237
Nb	Niobium	0.500	42.800	7.466	7.765	42.300	4.367	9.418	5.050	4.824	23.273	2.399	16.601
Nd	Neodynium	1.700	115.000	29.777	31.750	113.300	14.750	39.525	24.775	16.758	280.838	0.622	4.693
Ni	Nickel	1.000	360.000	16.972	7.000	359.000	5.000	13.000	8.000	38.253	1,463.294	5.983	44.099
Pb	Lead	0.890	83.450	21.688	21.000	82.560	11.060	28.000	16.940	14.544	211.517	1.344	6.139
Pr	Praseodymi	0.400	33.400	7.335	7.750	33.000	3.500	9.848	6.348	4.235	17.935	0.953	7.452
REE	La+Ce+Pr+Nd+Sm+Eu+Gd+Tb+Dy+Ho+Er+Tm+Yb+Lu	19.600	611.000	159.328	165.430	591.400	107.100	205.510	98.410	78.891	6,223.739	0.832	6.574
REEY	La+Ce+Pr+Nd+Sm+Eu+Gd+Tb+Dy+Ho+Er+Tm+Yb+Lu+Y	23.200	613.000	188.576	193.850	589.800	124.100	237.130	113.030	88.957	7,913.437	0.613	4.600
Rb	Rubidium	0.160	299.000	52.910	49.400	298.840	14.300	77.825	63.525	44.400	1,971.391	1.185	5.920
Re	Rhenium	0.000	0.003	0.002	0.002	0.003	0.001	0.002	0.002	0.001	0.000	-0.526	1.792
Sc	Scandium	2.200	67.800	15.465	16.200	65.600	9.325	19.675	10.350	8.300	68.898	1.108	8.482
Sm	Samarium	0.400	21.100	6.394	6.570	20.700	3.450	8.485	5.035	3.532	12.473	0.624	4.173
Sn	Tin	1.000	13.000	3.991	3.600	12.000	2.700	4.800	2.100	1.925	3.705	1.671	6.862
Sr	Strontium	2.000	1,600.000	334.182	320.500	1,598.000	170.000	467.750	297.750	212.895	45,324.213	1.012	6.965
Ta	Thallium	0.100	3.000	0.649	0.690	2.900	0.438	0.800	0.363	0.361	0.131	2.084	14.453
Tb	Terbium	0.100	2.930	0.882	0.870	2.830	0.600	1.100	0.500	0.486	0.236	1.103	5.576
Th	Thorium	0.470	57.020	12.542	11.850	56.550	5.640	16.200	10.560	9.130	83.359	1.437	6.382
Tl	Tantalum	0.030	10.000	1.942	0.715	9.970	0.362	1.510	1.147	3.123	9.753	2.131	5.782
Tm	Thulium	0.100	1.800	0.479	0.450	1.700	0.300	0.600	0.300	0.269	0.073	1.551	7.679
U	Uranium	0.150	12.000	3.610	3.650	11.850	1.625	5.018	3.393	2.255	5.083	0.541	3.219
V	Vanadium	2.000	460.000	111.060	118.000	458.000	50.000	150.000	100.000	71.213	5,071.349	0.961	5.959
Y	Yttrium	1.000	100.500	28.110	27.500	99.500	17.000	35.900	18.900	16.811	282.623	1.287	6.443
Yb	Ytterbium	0.200	11.900	3.217	3.080	11.700	1.975	4.102	2.128	1.879	3.531	1.259	6.361
Zn	Zinc	1.000	307.000	65.378	66.000	306.000	17.000	101.000	84.000	49.645	2,464.655	0.745	4.134
Zr	Zirconium	4.000	916.000	175.363	186.000	912.000	93.750	228.000	134.250	112.505	12,657.471	1.419	9.671

The most important statistics from this table is kurtosis. Kurtosis measures the combined weight of the tails of a distribution relative to its centre. In this way, we can use kurtosis as an indicator of the presence of outliers. A high kurtosis values is indicative of outliers. Validating the outliers will be easier with data visualisation, which will be presented in the next section.

The table below represents the descriptive statistics of elements from ME-4ACD81 test that will be used for predictive modelling.

1.3 Distribution Analysis

Next, we are going to analyse the distribution of each critical elements based on their PAAS normalised values. The Figure 1.1 provides insights regarding the spread, central tendency, and potential outliers for each critical element.

Figure 1.1: Distribution of Critical Elements (Box-Plot)

As depicted above, there are some key points that we would like to raise, which are:

• Medians: Most of the elements have their medians close to 0, indicating that the majority of the values are low or concentrated around a lower range. Considering that the threshold to define whether a sample is below/above background is 1, some elements that have median above the threshold are:

  Element Symbol	median
  Re	5.000
  Ag	3.600
  Au	3.333
  Mo	2.667
  Bi	2.402
  Li	2.000
  Cu	1.880
  Eu	1.648
  Dy	1.517
  Gd	1.513
  Sm	1.460
  Lu	1.438
  Yb	1.400
  Tm	1.364
  Tb	1.359
  MREE	1.344
  Er	1.320
  Ho	1.306
  U	1.304
  Ga	1.291
  Y	1.250
  Pb	1.235
  Nd	1.221
  Sc	1.191
  REEY	1.151
  REE	1.130
  Th	1.107
  V	1.103
  Pr	1.092
  LREE	1.064

• Spread and Variability: The elements exhibit varying degrees of spread. For example, Ge shows a wide range with its box stretching from a low value near 0 to a higher value around 10, indicating a large variability. On the opposite side, elements like Mn, Fe, Cr, Co, Rb, Ni, HREE have very narrow IQR, indicating less variability.
• Outliers: Several elements have significant outliers, as indicated by the dots outside the whiskers of the box plots. For instance, Ge, Bi, Mn, and Ba show notable outliers far from the main data range. Additionally, some elements that was reported from table 1.2, which have high kurtosis are Al, Ba, Bi, Ce, Co, Cr, Cs, Cu, Fe, Mn, Nb, and Ni. These outliers suggest the presence of some unusually high or low values for these elements, which could be of interest for further investigation.
• Symmetry and Skewness: Some elements like Ge, Bi, and Ag appear to have a right skew, with longer whiskers or outliers extending to the right, indicating that the distribution of their normalised values has a tail on the higher end. Elements like Ga and Sm show a more symmetrical distribution with whiskers extending fairly equally on both sides of the box.
• Comparison Accross Elements: Ge stands out with a particularly large spread and median, making it an outlier among the elements. Conversely, many rare earth elements (REE, REEY, MREE, LREE, HREE) have relatively low medians and a small spread, indicating that their normalised values are generally low and clustered.

The plot below represents the distribution of elements from ME-4ACD81 test that will be used for predictive modelling.

Figure 1.2: Distribution of Selected Critical Elements (Box-Plot)

1.4 Distribution of elements with reference to PASS levels

In this analysis, we are trying to assess all critical elements towards the PAAS standard. To begin with, we start from a high-level distribution across the two main categories that we use in identifying which elements that fall under above/below standard categories. The normalised value will be flagged as “Enriched above background” if it is above 1, while the rest will be flagged as “Below background”. The Figure 1.3 provide the details about this high-level distribution.

Figure 1.3: The Profile of PASS Categories

As depicted in the bar chart, the distribution appears fairly balanced between the two categories, with 5,724 instances classified as “Enriched Above Background” and 5,355 instances classified as “Below Background”. Such a balance highlights the importance of further detailed analysis to understand the factors contributing to this distribution, the significance of enrichment in the context of the dataset, and how these elements behave under different conditions.

Moving on to the element’s level, we will assess how each critical element’s PAAS level, whether they are above/below background value. The Figure 1.4 shows the profile of each sample towards this standard and their respective flags.

Figure 1.4: Distribution of elements with reference to PASS levels’ Concentration

As can be seen, the majority of normalised value fall within 0 to 10. Some highlight points from this plot are:

• Ag does not have any normalised PAAS values below background, indicating that coal waste is rich in Ag.
• HREE concentrations are always below background value.
• The significant differences in PAAS normalised value for some elements like Ge and Re needs further investigation as to why for a particular element that was sourced from coal and coal byproducts, such big gap could happen. In the later analysis, we will reveal if they are sampled from the same project area or they are actually sampled from different project area.
• All “below background” samples are actually just fall close to the threshold (between 0 and 1), indicating that coal and coal byproducts are highly potential as sources of these critical elements.

Furthermore, we also analyse how the distribution of the PAAS levels across various Project Area. The Figure 1.5 shows how many elements that was recorded in each project area fall into two categories.

Figure 1.5: The Profile of Project Area with reference to PASS levels’ Concentration

Some key observations from the plot are:

• The “Confidential_C” project stands out with a substantial number of elements (3,358) categorised as “Enriched Above Background”, significantly outnumbering the “Below Background” category count (1,192). This suggests a considerable concentration of elements that exceeded PAAS standard in this project.
• Project such as “Fort Cooper”, “Confidential_B” and “Confidential_A” display a more balanced distribution between two categories, indicating a near-equal mix of elements that either meet or fall short of the enrichment criteria.
• In contrast, several projects, such as “Wandoan”, “Copabella”, “Lake Vermont”, “Collinsville”, “Moorvalle”, “Newlands”, “Metropolitan”, “Rolleston” exhibit a higher count of elements classified as “Below Background”. This implies that these projects have a significant proportion of elements that do not reach the enrichment threshold.
• A few projects, including “Oaky Creek”, and “Unnamed”, contribute minimally to the overall dataset, with very few elements categorised in either categories.

Lastly, let’s see how is the distribution of each critical element on every project area. The Figure 1.6 below provide this information. As the continuation of the previous analysis, in this part we will focus more on the concentration of each element in each project area. For instance, such insights that we are going to look for are elements that have wide range of concentrations in one project, elements that have above/below background in the same project area.

Figure 1.6: Distribution of Critical Elements by Each Project Area

As shown by above graphs, some significant insights are:

• Collinsville: Co has wide range of concentration, which make some samples fall below background, while there is one sample that has high concentration, indicating that in one project area the same element can be significantly different.
• Confidential_A: the outlier of Tl that was seen in figure 1.1 and figure 1.4 is found here, suggesting high concentration of this element in this project area.
• Confidential_B: Outliers of multiple elements (Mo, Li, Cr, Ba) that were reported in figure 1.1 are spotted in this project area. This fact is relevant with the figure 1.5 where this project area was the source of many samples in our data. Additionally, we can spot a wide range of Ba concentration, in which one of the sample is categorised as “below background”, while there are two samples that categorised as “above background” with very high normalised value (above 10).
• Confidential_C: The same conditions as previous project area can be found in this project as well, where many outliers are found here considering many samples were taken in this project. Again, Ba also has a wide range of concentration, a substantial difference is spotted here, where one sample has high concentration value (above 10), while the rest are clustered together between 0 & 5.
• Fort Cooper: Majority of the elements’ concentration are between 0 & 10. However, we can see some elements which value are beyond 10, such as Mn, Ge, Bi, and Ag.
• Lake Vermont: Ba records significant concentration differences, where most of its sample are below background but one of them is very high (almost 18).
• Wandoan: It seems Ge are highly concentrated in this project area, because all of its samples taken from here have concentration beyond 10. This is also revealing where all of those outliers of Ge are located from, as reported in figure 1.1.

1.5 Correlation Matrix plot

Figure 1.7: Correlation Matrix Plot of Critical Elements

The figure 1.7 shows the relationships between various elements. Some key observations are:

• Strongly positive correlations: There are numbers of elements that have very strong relationship (above 0.95), such as Er-Dy, Gd-Eu, Ho-Dy, Ho-Er, Pr-Nd, Sm-Nd, Tb-Dy, Tb-Gd, Tb-Ho, Yb-Er, and Yb-Ho. There are also many more elements that have correlation above 0.8.
• Moderate correlations: Many elements fall between 0.6-0.8, which indicate fairly strong relationships.
• Weaker Correlations: Elements such as Ba show weaker correlations with most other elements, indicating less consistent co-occurrence or independent behavior within the dataset.This also the case for Sr.

The correlation matrix plot below represents the matrix of elements from ME-4ACD81 test to REE, HREE, and LREE. This is to understand the correlation between all elements to the target variable as part of the predictive modelling.

Figure 1.8: Correlation Matrix Plot of Selected Critical Elements

1.6 Scatter Plot

In this last section, we are going to dig deeper into critical elements that have correlation value above 0.95 (as mentioned in the previous points). For context, Er, Dy, Gd, Eu, Ho, Pr, Nd, Sm, Tb, and Yb are known as lanthanides series. Lanthanides are a group of the first 15 f-block elements with atomic numbers from 57 to 71. In addition to yttrium, which share many similar chemical properties with the lanthanides, these elements comprise the rare earth elements (REEs) (Mattocks et al., 2021). Their high correlation values are most likely affected due to this fact.

Furthermore, Seredin (2012) suggest that the first suggestions for recovering lanthanides and yttrium (REY) as by-products from coal deposits can be traced back to 20 years ago, following the discovery of coal beds in a Russian Far East (RFE) basin that had high REY content (0.2% - 0.3%). Additional coal seams with comparable or even higher REY concentrations (up to 1.0% in ash) were identified in six coal-bearing basins across the same region. Since then, REY-rich coal has also been discovered in coal basins in various other countries. Thus, the lanthanides are found in coal and coal by-products could be possible because of their association with the materials that make up coal.

Correlated element (Above 0.95)

Figure 1.9: Strongly Correlated Critical Elements

The Figure 1.9 above depicted show correlations between these elements, additional colour dimension was added to differentiate the project areas. In summary, there are many correlations that closely align to each other, as shown by the tight spread of the dot points around the straight line, which are exhibited by Pr & Nd, Gd & Eu, Ho & Er, Tb & Dy, Yb & Er, Sm & Nd, and Sm & Pr plots. In some of the plots, there are a few data points that deviate from the majority of the points. These could be potential outliers or cases where the relationship slightly diverges, which are exhibited by Er & Dy, Ho & Dy, Yb & Dy, Yb & Ho, Tb & Ho, Tb & Gd plots. For Sm & Nd, and Sm & Pr plots even though they are belong to the previous group, but when we look closely from the project area point of view, we can see that the grey dots (which represents ‘Wandoan’) are deviating away from the linear line. This indicates the correlation between them are not strong. Let’s dig deeper into these elements by utilising plots below.

Figure 1.10: Correlated Critical Elements (Sm, Pr, Nd) in Wandoan

As can be seen in the correlation matrix of figure 1.10, in Wandoan, the correlation between Sm and Nd is 0.95, just right at the minimum threshold that we chose. However, Sm and Pr correlation is below 0.95, which contributes to the fact that the points deviate away from the linear line. Considering their correlation value is below our threshold, it’s most likely that Sm and Pr correlation from this project is excluded for the predictive modelling part.

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